Season short ribs and pork belly all over with salt and pepper. In a large, heavy-bottomed stockpot, heat oil over medium-high heat until shimmering. Working in batches to avoid crowding the pot, add beef and pork belly and cook, turning, until browned all over, about 5 minutes per side. Transfer meats to a rimmed baking sheet or platter and set aside. Add onion, carrot, celery, and garlic to pot and cook, stirring and scraping up any browned bits, until starting to brown, about 6 minutes.,Stir in tomato paste and cook for 2 minutes, lowering heat if necessary to prevent scorching. Add 4 quarts (3.75L) water, short ribs, pork belly, marrow bones, ham hock, dill, parsley, and bay leaf and bring to a simmer over medium-high heat. Lower heat to maintain a gentle simmer and cook until meats are tender, about 3 hours.,Strain meat broth, reserving all meats and bones; discard vegetables. You should have about 3 quarts (2.8L) broth. If you have less, add enough water to bring it up to 3 quarts. You can refrigerate broth and meats separately for up to 3 days before continuing with the recipe, or continue immediately.,Pick bones from short ribs and ham hocks and push marrow from bones. Discard bones. Cut up all broth meats and marrow into small dice and set aside. (If marrow is hot, it won't dice neatly; this is fine.) Skim rendered fat from surface of broth (if broth is cold, the fat will be a solid cap on top); reserve 1/4 cup (60ml) and discard the rest.,In a large, heavy-bottomed stockpot, heat the 1/4 cup reserved fat from broth over medium-high heat until shimmering. Add onion, carrot, celery, and garlic and cook, stirring, until softened, about 5 minutes. Add 3 quarts (2.8L) meat broth and bring to a simmer.,______,Stir toasted caraway, if using, into sour cream and season lightly with salt. Ladle hot borscht into bowls and top with dollops of caraway sour cream and fresh dill. Serve right away. Remaining soup can be refrigerated for up to 5 days and frozen for up to 3 months.